Question

Evaluate the following sum:

$S=\left(\underset{20terms}{\underset{}{190+167+144+121+\dots }}\right)$ [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

We do not know the last term in this sequence, so we will use the first formula to calculate this sum. We note that:

$a=190,d=-23,n=20$

$S=\frac{n}{2}(2a+(n-1\left)d\right)$

$S=\frac{20}{2}\left(2\right(190)+(20-1\left)\right(-23\left)\right)$

$=10(380-437)$

$=10(-57)$

$=-570$